






'''simple docstring'''







def       __UpperCamelCase					(      lowercase_       :  int   ,       lowercase_       :  list   ):
       """simple docstring"""




       _enforce_args(lowercase_   ,       lowercase_   )
       if n == 0:
              return 0
       a_						     =			float('-inf'   )
       for i in range(1   ,       n + 1   ):
              a_						     =			max(
                  lowercase_   ,       prices[i - 1] + naive_cut_rod_recursive(n - i   ,       lowercase_   )   )

       return max_revue


def       __UpperCamelCase					(      lowercase_       :  int   ,       lowercase_       :  list   ):
       """simple docstring"""




       _enforce_args(lowercase_   ,       lowercase_   )
       a_						     =			[float('-inf'   ) for _ in range(n + 1   )]
       return _top_down_cut_rod_recursive(lowercase_   ,       lowercase_   ,       lowercase_   )


def       __UpperCamelCase					(      lowercase_       :  int   ,       lowercase_       :  list   ,       lowercase_       :  list   ):
       """simple docstring"""




       if max_rev[n] >= 0:
              return max_rev[n]
       elif n == 0:
              return 0
       else:
              a_						     =			float('-inf'   )
              for i in range(1   ,       n + 1   ):
                     a_						     =			max(
                         lowercase_   ,       prices[i - 1] + _top_down_cut_rod_recursive(n - i   ,       lowercase_   ,       lowercase_   )   ,       )

              a_						     =			max_revenue

       return max_rev[n]


def       __UpperCamelCase					(      lowercase_       :  int   ,       lowercase_       :  list   ):
       """simple docstring"""




       _enforce_args(lowercase_   ,       lowercase_   )

       # length(max_rev) = n + 1, to accommodate for the revenue obtainable from a rod of
       # length 0.
       a_						     =			[float('-inf'   ) for _ in range(n + 1   )]
       a_						     =			0

       for i in range(1   ,       n + 1   ):
              a_						     =			max_rev[i]
              for j in range(1   ,       i + 1   ):
                     a_						     =			max(lowercase_   ,       prices[j - 1] + max_rev[i - j]   )

              a_						     =			max_revenue_i

       return max_rev[n]


def       __UpperCamelCase					(      lowercase_       :  int   ,       lowercase_       :  list   ):
       """simple docstring"""




       if n < 0:
              a_						     =			F'n must be greater than or equal to 0. Got n = {n}'
              raise ValueError(lowercase_   )

       if n > len(lowercase_   ):
              a_						     =			(
                  'Each integral piece of rod must have a corresponding price. '
                  F'Got n = {n} but length of prices = {len(lowercase_   )}'
              )
              raise ValueError(lowercase_   )


def       __UpperCamelCase					(      ):
       """simple docstring"""




       a_						     =			[6, 10, 12, 15, 20, 23]
       a_						     =			len(lowercase_   )

       # the best revenue comes from cutting the rod into 6 pieces, each
       # of length 1 resulting in a revenue of 6 * 6 = 36.
       a_						     =			36

       a_						     =			top_down_cut_rod(lowercase_   ,       lowercase_   )
       a_						     =			bottom_up_cut_rod(lowercase_   ,       lowercase_   )
       a_						     =			naive_cut_rod_recursive(lowercase_   ,       lowercase_   )

       assert expected_max_revenue == max_rev_top_down
       assert max_rev_top_down == max_rev_bottom_up
       assert max_rev_bottom_up == max_rev_naive


if __name__ == "__main__":
  main()












'''simple docstring'''







from __future__ import annotations

from collections.abc import Iterator
from typing import Generic, TypeVar

__lowerCAmelCase        =							TypeVar("T")




class   __SCREAMING_SNAKE_CASE       (Generic[T]       ):


  """simple docstring"""


  def __init__(			self   ,	UpperCamelCase__	):






         """simple docstring"""


         a_						     =			data
         a_						     =			None







  def __str__(			self	):






         """simple docstring"""


         return f'{self.data}'





class   __SCREAMING_SNAKE_CASE       (Generic[T]       ):


  """simple docstring"""


  def __init__(			self	):






         """simple docstring"""


         a_						     =			None







  def __iter__(			self	):






         """simple docstring"""


         a_						     =			self.top
         while node:
                yield node.data
                a_						     =			node.next







  def __str__(			self	):






         """simple docstring"""


         return "->".join([str(UpperCamelCase__	) for item in self]	)







  def __len__(			self	):






         """simple docstring"""


         return len(tuple(iter(self	)	)	)







  def    _a       (			self	):






         """simple docstring"""


         return self.top is None







  def    _a       (			self   ,	UpperCamelCase__	):






         """simple docstring"""


         a_						     =			Node(UpperCamelCase__	)
         if not self.is_empty():
                a_						     =			self.top
         a_						     =			node







  def    _a       (			self	):






         """simple docstring"""


         if self.is_empty():
                raise IndexError('pop from empty stack'	)
         assert isinstance(self.top   ,	UpperCamelCase__	)
         a_						     =			self.top
         a_						     =			self.top.next
         return pop_node.data







  def    _a       (			self	):






         """simple docstring"""


         if self.is_empty():
                raise IndexError('peek from empty stack'	)

         assert self.top is not None
         return self.top.data







  def    _a       (			self	):






         """simple docstring"""


         a_						     =			None


if __name__ == "__main__":
  from doctest import testmod

  testmod()




